Analysis of microstrip resonators of arbitrary shape.pdf

112 IEEE TRANSACTIONS ON MICROWAVE THEORY A N D TECHNIQUES, VOL 40. NO I . JANUARY 1992 Analysis of Microstrip Resonators of Arbitrary Shape Krzysztof A. Michalski, Senior Member, IEEE, and Dalian Zheng, Member, IEEE Abstract-A space-domain approach based on a mixed-poten- though the rectangular-mesh model has successfully been tial integral equation formulation is developed for efficient used to analyze planar microstrip structures of various computation of complex resonant frequencies of laterally open shapes [ 111-[13], a triangular-element model is applica- microstrip-patch resonators of arbitrary shape. The effects of the substrate-which may consist of any number of planar, ble to a still wider class of geometries. This has recently possibly uniaxially anisotropic, dielectric layers-are rigor- been recognized by several authors [14]-[ 161, who em- ously incorporated in the formulation by means of the vector ployed the MPIE formulation in conjunction with the vec- and scalar potential Green’s functions. The current distribu- tor basis functions defined over a triangular support [ 171. tion on the conducting patch is approximated in terms of vector In this paper, we adopt the latter approach to study lat- basis functions defined over triangular elements. Computed resonant frequencies, quality factors, modal currents, and far- erally open microstrip resonators of planar, but otherwise field radiation patterns are presented for sev